I want to bury my garden lighting cable in conduit what size conduit is needed to allow pulling of 12 2 direct barrel low voltage lighting wire.

3/4" should be fine.

Is your cable listed for underground use? The outside ground is considered as a ":Wet" area. Therefore, cable, even if it is in a conduit has to listed for unse underground.

Also, just curious, how much voltage and amperage is this cable coing to carry.